Subsurface exploration, and in particular exploration for hydrocarbon reservoirs, typically uses methods such as migration of seismic data to produce interpretable images of the earth's subsurface. In areas where the subsurface is complex due to faulting, salt bodies and the like, traditional migration methods often fail to produce adequate images. Additionally, traditional migration methods require a reasonably accurate velocity model of the subsurface; such velocity models may also be determined from the seismic data but may be very expensive in both expertise and computational cost.
There are many conventional methods for computing velocity models from seismic data, including NMO velocity analysis, migration velocity analysis, tomography, and full waveform inversion. Some methods, such as full waveform inversion, are very computationally expensive and have only recently become practical as computing power has increased. Conventional full waveform inversion is done in the time domain or in a transform domain such as the temporal Fourier transform domain or the Laplace transform domain. These methods often fail due to the lack of low frequencies, typically less than 3 Hertz, in seismic data. As one skilled in the art will appreciate, a velocity model is a low frequency model so it is difficult to invert for it from the seismic data that lacks the low frequency information.
Traditional methods of determining velocity models and using them for migration to produce images of the earth's subsurface are expensive and fraught with difficulties, especially in complex areas. As the search for hydrocarbons moves to these complex areas, it is necessary to find better ways to process the seismic data and improve velocity models.